A Geometric Combination Estimator for $d$-Dimensional Ordinal Sparse Contingency Tables
多维有序稀疏列联表的几何组合估计
A geometric combination estimator is proposed for $d$-dimensional ordinal contingency tables. The proposed estimator is nonnegative. It is shown that, assuming sufficient smoothness and boundary conditions for the underlying probabilities, the rate of convergence of mean summed squared error (MSSE) of this estimator is $O(K^{-1}N^{-8/(d+8)})$ for $d$-dimensional tables $(d \leq 4)$ with $K$ cells and sample size $N$. This rate is optimal under the smoothness assumptions, and…